Characterization of resolution cycle times of corrective actions in mobile terminals

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1 Powered by TCPDF ( This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Mwegerano, A.; Kytösaho, P.; Liukkonen, T.; Tuominen, A. Title: Characterization of resolution cycle times of corrective actions in mobile terminals Year: 2008 Version: Final published version Please cite the original version: Mwegerano, A., Kytösaho, P., Liukkonen, T., Tuominen, A Characterization of resolution cycle times of corrective actions in mobile terminals. Quality and Reliability Engineering Internal Journal, 24 (1), pp Note: John Wiley and Sons, Ltd Reprinted with permission. This publication is included in the electronic version of the licentiate thesis: Mwegerano, Andi Mawazo. Handling Customer Complaints during the After-Sales Service: Mobile Terminals. Aalto University, School of Electrical Engineering app. 50. All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user.

2 QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL Qual. Reliab. Engng. Int. 2008; 24: Published online 1 April 2008 in Wiley InterScience ( Case Study Characterization of Resolution Cycle Times of Corrective Actions in Mobile Terminals Anderson Mwegerano 1,,, Pekka Kytösaho 1, Timo Liukkonen 1 and Aulis Tuominen 2 1 Nokia Corporation, P.O. Box 86, FIN Salo, Finland 2 University of Turku, Ylhäistentie 2, Salo, Finland Resolution cycle times for resolving issues raised by customers is one of the essential factors for indication of the customer s satisfaction. The fact that there are many mobile terminals manufacturers implies that competition to grab and hold market share for a sustainable time is very strong. A forecasting model, based on a selected statistical distribution, is built up to give an estimation of the resolution time in three different category products. In this paper the model does not specify different failure symptoms reported by customers. Uncertainties and the reliability of the model buildup are discussed and example of an optimized correction action is given. Copyright 2008 John Wiley & Sons, Ltd. Received 13 February 2008; Accepted 14 February 2008 KEY WORDS: optimizing; resolution cycle times; corrective actions; issues; customers 1. INTRODUCTION The analogue system known now as the 1G system was the first popular mobile phone. The digital system known as the 2G system was launched in the early 90s. The 3G system has been introduced in the early 2000s and is still migrating. The growth of mobile phones has been expanding exponentially. In 1981 there were mobile telephone users and in the year 2004 there were ca. 1.6 billion users (Figure 1) 1. There is enormous strong competition among the cellular mobile phone manufacturers. To hold or increase the market share requires sustainable efforts compared with competitors. Other important aspects that will help to capture the market, are: customer satisfaction, short delivery time, loyalty and short resolution times for issues of concern to customers 2. This paper attempts to discover the main causes for long resolution times. A forecasting model, based on a selected statistical distribution, was built to give an estimation of the resolution time in three product categories. Correspondence to: A. Mwegerano, Nokia Corporation, P.O. Box 86, FIN Salo, Finland. andi.mwegerano@nokia.com Copyright q 2008 John Wiley & Sons, Ltd.

3 614 A. MWEGERANO ET AL. Figure 1. Handset users growth 1 CA L1 CA L2 CA L3 CA L4 CUSTOMER CA Corrective Actions L Level 1, 2, 3 & 4 Figure 2. A simplified issues escalation path diagram 2. ANALYSING CURRENT STATE ANALYSIS Data was collected from three products within three product categories, product 1 was the simplest and product 3 the most complex. Customers could receive a new swap phone if the duration of the resolution time exceeded a pre-set time limit (Figure 2). 3. ANALYSIS PROCEDURE USED The best distribution model was selected with the maximum likelihood method 3. The maximum likelihood estimates of the parameters in the distribution are calculated by maximizing the likelihood function with respect to the parameters. For a given data set, the likelihood function of a distribution describes the chance of generating the data set. When we assume that our data follow a specific distribution, we take a serious risk. If our assumption is wrong, then the results obtained may be invalid. One way to deal with this problem is to check the distribution assumptions carefully. There are two main approaches to checking distribution assumptions. One involves empirical procedures, which are easy to understand and implement and are based on intuitive and graphical properties of the distribution. There are also statistical procedures for assessing the underlying distribution of a data set. These are the goodness-of-fit tests. They are numerically convoluted and usually require specific software for lengthy calculations. But results are quantifiable and more reliable than those from empirical procedures 4. The Newton Raphson algorithm is used to calculate maximum likelihood estimates of the parameters, which define the distribution. The Newton Raphson algorithm is a recursive method for computing the maximum of a function. The percentiles are calculated from that distribution. For computations, see Reference 5. An Anderson Darling test assesses whether a sample comes from a specified distribution. The Weibull distribution was selected due to its lowest Anderson Darling value in the goodness-of-fit test in the Minitab Statistical Analysis software release (Table I). Alternative to Anderson Darling one could also implement the Kolmogorov Smirnov test for goodness of fit 4.

4 CHARACTERIZATION OF RESOLUTION CYCLE TIMES 615 Distribution Table I. Goodness-of-fit Anderson Darling (Adjusted) Weibull Lognormal Exponential Loglogistic Parameter Weibull Parameter lognormal Parameter exponential Parameter log logistic Smallest extreme value Normal Logistic Definition of the Weibull distribution 5. Weibull distribution: pdf: ( β ( x ) ) β α β (x)β 1 exp α cdf: [ ( x ) ] β 1 exp α Mean: St.dev.: α 2 (Γ ( αγ 1+ 1 ) β ( 1+ 2 ( ) Γ )) β β where α is the shape parameter and β the scale parameter. Figures 3 and 4 show two Weibull distributions applied to the data about case resolution times by products and corrective actions. Product 3 (most complex) and corrective action A pop up clearly from the figures. 4. CORRECTIVE ACTIONS Corrective action categories were analysed more deeply to give insight into the possibilities there are to optimize total resolution time. A pareto chart is one of the most widely used tool to prioritize drill-down opportunities 5. Figure 5 shows that corrective action A has major impact separately compared with others, and Figure 6 shows that this is not only clear especially in product 3 but remarkable also in the other two products Simple correspondence analysis: corrective action category and product Statistical independency of characteristics can also be determined by contingency tables 1. Thus, it can be observed from Table II that 84% of the total variation is described by the first axis and is also seen in Figure 8 as the first component in the graph.

5 616 A. MWEGERANO ET AL. Figure 3. Distribution of resolution time by products Figure 4. Distribution of resolution times by corrective actions category Figure 5. Pareto of corrective actions (A to E+ others) categories

6 CHARACTERIZATION OF RESOLUTION CYCLE TIMES 617 Figure 6. Paretos of corrective actions by product Table II. Analysis of contingency table Axis Inertia Proportion Cumulative Total Figure 7. Simple correspondence analysis of corrective action category and product 8 Figure 7 explains better how good the corrective actions are associated with different products, i.e. corrective actions A and F are most seen in product 3, whereas corrective action E is most seen in product 1. Corrective actions BDC are more associated with product 2. Box plot is a tool that can visually show differences between characteristics of a data set. Box plots display the lower and upper quartiles (the 25th and the 75th percentiles), and the median (the 50th percentile)

7 618 A. MWEGERANO ET AL. Figure 8. Box plots of time units in CA levels appears as a horizontal line within the box 5. From the above box plot (Figure 8) it can be observed that: 1. Most data flow is between L2 and L4 in all the three products. 2. L3 is almost a data path through passage. 3. L1 is observed to be active in product Corrective action category B is predominantly seen in L2 in all the three products. 5. Corrective action category A is predominantly seen in L4 in all the three products.

8 CHARACTERIZATION OF RESOLUTION CYCLE TIMES Principal component analysis Principal component analysis (PCA) provide a roadmap for how to reduce a complex data set to a lower dimension to reveal the sometimes hidden, simplified structure that often underlie it 6. The eigenvalues of the used levels (the same levels as used before in Figure 8) define the variance of the principal components. The first principal component accounts for the largest percentage of the total data variation. The second principal component accounts for the second largest percentage of the total data variation, and so on. The goal of the principal components is to explain the maximum amount of variance with least number of components. If the eigenvalue is <1 the component is not important, which is the case with component numbers 3, 4 and 5 (see Figure 9) 7,8. Figure 10 tells about two principal components i.e. data structure of the process. The first component tells about the 84% data variation, whereas the second component tells about the 2nd variation, which does not depend on the first component. This figure contains the same information as in the box plots of Figure 8, but explains in a more vivid way as only few components are selected. From the principal component analysis (Figure 10), it can be observed that: 1. L2 and L4 are closely correlated. 2. L3 is correlated to L1 and L4 but not L2. Figure 9. Eigenvalues of levels 7 Figure 10. Principal component analysis of levels 7

9 620 A. MWEGERANO ET AL. Table III. Weibull parameters Product Corrective action category Shape Scale 1 A B C * * 1 D * * 1 E F A B C D E * * 2 F A B C D E F Figure 11. Histogram comparison before and after optimization at L2 and CA B 5. MODEL SET-UP Corrective actions at L2 and L4 are the major contributors to the total resolution time. The optimization should be focused in L2 on Corrective Action category B (CA B) and in L4 on category A and C (CA A and CA C) respectively. In the most complex product (product 3), one should additionally focus on L1, as CA A is contributing most to it. If the optimization succeeds, a new resolution time can be simulated with the desired Weibull shape and scale parameters (see Table III). For example, L2 and CA B, with desired shape and scale would give the following distribution before and after optimization (Figure 11).

10 CHARACTERIZATION OF RESOLUTION CYCLE TIMES 621 Figure 12. Weibull with 90% confidence intervals 6. RESULTS AND DISCUSSIONS Minor differences were found between corrective actions from three products with different complexities; nevertheless, the model can be considered universal. The procedure can and should be separately applied in forthcoming products to point out improvement needs and to optimize resolution times. Weibull was found to be the best-fitting distribution in this case, as expected. To reduce resolution time, one should focus on the right tail areas of the distribution and corrective actions should be investigated (Figure 12). The fitting is good enough in the right tail areas with 90% confidence interval. Uncertainties of no interest to this paper exist in the left tail of the fitting. REFERENCES 1. [22 May 2005]. 2. Koskela H. Customer satisfaction and loyalty in after sales service: Modes of care in telecommunications systems delivery. PhD Dissertation, Helsinki University of Technology, Hair A, Tatham B. Multivariate Data Analysis (5th edn). Prentice-Hall: Englewood Cliffs, NJ, Romeu JL. Anderson Darling: A goodness of fit test for small samples assumptions. START Selected Topics in Assurance Related Technologies 2008; 10(5). Available at: DTest.pdf. [22 January 2008]. 5. Breyfogle FW. Implementing Six Sigma (2nd edn). Wiley: New York, Shlens J. A tutorial on principal component analysis. shlens/pub/notes/pca.pdf. [22 January 2008]. 7. MINITAB R Release Manual (Six Sigma Academy Module Release 14.13). 8. Murray W (ed.). Numerical Methods for Unconstrained Optimization. Academic Press: New York, 1972.